\section{Production of $\ca{48}$}
\label{appendix:ca48}

The short beta-decay half of $^{45}$Ca
(162.2 days) and even shorter half of $^{47}$Ca (4.536 days)
prevent $^{48}$Ca from being produced in the same environment.  The
site of $^{48}$Ca synthesis is suspected to be a subset of
thermonuclear supernovae (type Ia supernovae)
that achieve high enough densities to have significant electron capture
during the explosion (e.g., \cite{1996ApJ...462..825M,1997ApJ...476..801W}).
Because the matter in these explosions has low entropy per nucleon
(typically less than 0.1 $k_B$, where $k_B$ is Boltzmann's constant,
per nucleon), the nuclear abundances are characterized by an overabundance
of heavy nuclei relative to nuclear statistical equilibrium.  This permits
production of abundant $^{48}$Ca when nuclear statistical equilibrium would
require even larger production of $^{66}$Ni, an isotope with nearly
the same degree of neutron richness \cite{1985ApJ...297..837H}.  

Neither s-process or r-process could not produce $\ca{48}$ as shown in the
figures below.

\begin{figure}[ht!]
\centering
  \includegraphics[width=1.\textwidth]{figures/s1}
\caption{S-process production}
\label{fig:s1}
\end{figure}

\begin{figure}[htb]
\centering
  \includegraphics[width=1.\textwidth]{figures/s2}
\caption{S-process production}
\label{fig:s2}
\end{figure}

\begin{figure}[htb]
\centering
  \includegraphics[width=1.\textwidth]{figures/s3}
\caption{S-process production}
\label{fig:s3}
\end{figure}

\begin{figure}[htb]
\centering
  \includegraphics[width=1.\textwidth]{figures/s4}
\caption{S-process production}
\label{fig:s4}
\end{figure}

\begin{figure}[htb]
\centering
  \begin{tabular}{c}
    \includegraphics[width=1.\textwidth]{figures/r1} \\
    \includegraphics[width=1.\textwidth]{figures/r2} \\
    \includegraphics[width=1.\textwidth]{figures/r3} \\
    \includegraphics[width=1.\textwidth]{figures/r4} \\
  \end{tabular}
\caption{R-process production}
\label{fig:r-process}
\end{figure}
